Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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Description
ELASTOMEP~IC HIGH TO~UE
CONSTANT VELOCITY JOINT
Technical ~ield
This invention relates to a high torque, constant
velocity joint employing elastomeric bearing
technology.
Background
Constant velocity (homokinetic) joints accommodate
angular misalignment (tilt) between the axes of a rotating
drive and load without pulsations in the load such as
are inherent in a Hooke (or Cardan) joint. In other
words, there is constant positional correspondence
between the drive and the load. One type of constant
velocity joint that can handle high torque loads uses
grooved inner and outer spherical metallic races with
ball bearings riding therebetween. These joints are
complex and expensive.
Elastomeric bearings, comprising bonded-together,
alternate layers of elastomer and shims, provide
numerous advantages over conventional (metallic)
bearings. "Since these bearings accommodate motion by
simple flexing of their elastomer laminates, there are
no rolling or sliding elements as in more conventional
bearings. No lubrication or servicing of any kind is
required. Seals, boots, or dust covers are not
needed and there is no friction or wear. The result
is a bearing system which provides extremely long life,
and which requires no maintenance of any kind. In
S-3770 ~`
1,2~3~9
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addition, a simple ~isual inspection of the bearing's
surface at periadic inter~als is sufficient to determine
the bearing's condition." (American Helicapter Society
Journal, January 1981, p.34; The Sikorsky Elastomeric
Rotor, R. Rybicki).
Typical materials for an elastomeric bearing
include rubber compounds, such as 85% natural rubber
and 15% polybutadiene for the elastomer and stainless
steel for the shi~s.
An example of a constant velocity joint using
elastomeric bearing techniques is disclosed in U.S.
Patent No. 4,208,889 (Peterson, 1980), entitled
CONSTANT VELOCITY, TORSIONALLY RIGID, ~LE~IBLE
COUPLING. That example suffers from complexity,
requiring a plurality of connecting members and at
least as many separate elastomeric bearings.
Another elastomeric constant velocity joint is
disclosed in U.S. Patent No. 3,524,332 ~Callies, 1968),
entitled ELASTOMER COUPLING. Therein the drive is
through an annular elastomer element. The ability of
such a coupling to transmit torque is limited not only
by the separation of the elastomer element from its
associated hub, but more fundamentally, by the low
shear modulus of the elastomer since this example
reacts torque in shear.
Disclosure of The In~ention
Therefore it is an object of this invention to
provide a cons~ant velocity joint which is capable of
transmitting large torques while accommodating
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~463~g
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angular misalignment between a drive and a load, and
that benefits from elastomeric bearing technology.
In accordance with the broad aspects of the
invention, there is provided a constant velocity joint
which includes an inner shell having an exterior sur-
face defined by an axis. At least three arc segments
generate points equally offset from the axis and sym-
metrically distributed thereabout on a plane which is
normal to the axis, and a first radius extends from
each of the at leas`t three arc segment generating
points. The exterior surface has a nearly spherical
axial profile with polar symmetry. An outer shell is
disposed about the inner shell and has an interior sur-
face defined by the axis and the at least three arc
segment generating points and a second radius larger
than the first radius from each of the at least three
arc segment generating points. The interior surface
has a nearly spherical axial profile with polar
symmetry. At least one elastomer layer is disposed
between the exterior surface of the inner shell and the
interior surface of the outer shell and alternate
layers of shims between the elastomeric layers in the
case of more than one elastomeric layer. The elasto-
meric layers are bonded to the respective exterior
surface of the inner shell and interior surface of the
outer shell and to the shims.
According to the invention, a nearly
spherical elastomeric bearing has an inner shell, an
outer she]l, and bonded-together, alternate ]ayers of
elastomer and nonresilient shims interposed at increas-
ing radii therebetween. The bearing is rotatable about
63~9
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a longitudinal axis and has two axial ends. Axial
deviations from true sphericity (lobes) give the bear-
ing a noncircular latitudinal (transverse) cross-
section, particularly at an equatorial plane which is
5 normal to the axis and midway between the ends. The
lobes cause applied torque to be reacted by elastomer
bending (tension and compression normal to each layer)
rather than by in-plane shear. The tensile stresses
produced by elastomer bending are reduced by bearing
precompression. Gn the other handr the profile of the
bearing is nearly spherical so that the bearing is very
compliant in tilt via elastomer shear. Both ends of
the bearing are truncated (open) - one for attachment
of a rotatable drive member to the inner shell, and the
other for polar symmetry, which is necessary for homo-
kineticity. A rotatable load member is attached to the
outer race of the bearing so that the bearing of this
invention functions as a flexible jointA
The joint of this invention is useful in the
context of a gimbal-like rotor system wherein it drives
torque from the rotorshaft to the blades as well as
accommoda-ting blade flapping. However, improvements to
the joint are disclosed in commonly owned U.S. Patents
4,575,358 and 4,676,669 which make the joint even more
useful for that application.
Other objects, features, advantages and
applications of the invention will become apparent in
light of the following description of several embodi-
ments and the accompanying drawings.
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Brief Description of The Drawings
Fig. I is a perspective view of an embodiment of
the bearing of thîs in~ention;
Fig. 2 is a transverse cross-sectional view of
the bearing of ~ig. 1 through its equatorial plane
with a hydrostatic pressure pattern superimposed thereon;
Fig. 3 is a transverse cross-sectional view of a
bearing of the priar art,
Fig. 4 is a transverse cross-sectional view of a
model bearing segment, in unloaded (4a) and torsionally
loaded (4b) states, which highlight certain principles
involved in the bearing of Figs. 1 and 2;
Fig. 5 is a transverse cross-sectional view of an
alternate embodiment of the bearing of this invention
through its equatorial plane with a hydrostatic pressure
pattern superimposed thereon;
Fig. 6 is a transverse cross-sectional view of a
model bearing segment, in unloaded (6a) and torsionally
loaded (6b) states, relating to the embodiment of Fig. 5.
Fig. 7 is a cross-sectional view of a constant
velocity joint using the bearing of this invention.
Fig. 8 is an isometric view of the bearing of Fig. 1
incorporating modifications;
Fig. 9 is a partial transverse cross-sectional view
of the bearing of Fig. 2 incorporating modifications;
Fig. 10 is a partial transverse cross-sectional
view of the bearing of Fig. 2 incorporating modifications;
Fig. 11 is a perspective, partial cutaway view of
a helicopter gimbal-type rotor system employing the
bearing of this invention; and
Fig. 12 is an axial (vertical) section of the
bearing shown in Fig. 11.
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Best Mode For Carrying Out The Invention
TORSIONAL STIFFNESS
In Fig. 1 is shown an embodiment of the
elastomeric bearing 10 of this invention comprising an
inner shell 12, an outer shell 14, and alternate layers
of an elastomer 16 and nonresilient shims 18 interposed
therebetween at increasing radii. The number of layers
is not limited to -the number shown and could even be a
single layer of elastomer with ro shims. The overall
shape of the bearing is nearly spherical, having a
longitudinal axis of rotation 20. The bearing 10 is
open at at least one axial end for connecting a rota-t-
able drive or load member to the inner race 12. As
shown, the bearing 10 is open at both ends for polar
symmetry, thereby defining an upper edge 22 and a lower
edge 24. An axial height is defined between the edges
22 and 24. The bearing 10 is not a true sphere due to
longitudinal lobes or eccentricities 25 distributed
about it 9 azimuth.
The lobes 25 result from the noncircular
transverse cross-section of the bearing - best viewed
in Fig. 2, which is a cross-section of the bearing 10
on an equatorial plane which is normal to the axis and
midway between the ends. As described hereinafter, the
transverse cross-section of the elastomer layers 16 is
especially important to the bearing's ability to trans-
mit high torque loads and results essentially from the
transverse contours of the exterior (elastomer-facing)
surface of the inner shell 12 and the interior
(elastomer-facing) surface of the outer shell 14.
~4~3~g
The transverse contour of the interior
surface of the inner shell 12 is defined by a radius
(Rl) from each of four arc segment generating points
26-29 which are equally offset from the axis 20 and
symmetrically ~istributed (every ninety degrees,
azimuthally) thereabout. The radius (Rl) is greater
than the distance from the inner shell 12 to the axis
20. Therefore, the transverse contour oE the exterior
surface of the inner shell 12 is four intersecting non-
concentric arc-segments 30-33, the intersections of
which are four outwardly-extending lobes 34-37 which
are symmetrically distributed about the azimuth of the
bearing. Similarly, the transverse contour of the
interior surface of the outer shell 14 is defined by a
radius (R2), which is greater than the radius (Rl) by
the combined thicknesses, of the elastomer 16 and shims
18, from the points 26-29. Four outwardly-extending
lobes 38-41 are thereby defined in register
(azimuthally) with the lobes 34-37 of the inner shell
12, respectively. The transverse contours of the
exterior (facing away from the e]astomer 16) surface of
the shell 12 and interior (facing away from the
elastomer 16) surface of the shell 14 are not parti-
cularly germane to an understanding of the invention
and may be adapted to couple to a drive member and a
load member, in any suitable manner, such as that des-
cribed hereinafter with reference to Fig. 7.
The cross-section of a particular elastomer
layer or shim would be defined by an appropriate
radius, having a magnitude larger than (Rl) and less
than (R2), from the points 26-29, and a thickness.
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As mentioned hereinbefore, the torque-handling
capability of the bearing derives from the transverse
cross-sections of the elastomer layers 16 and is best
understood by reference to two models.
The first model is a spherical or cylindrical
radial ~earing of the prior art, either of which has
a circular transverse cross-section as shown in ~ig.
3. Therein a layer 44 of elastomer is disposed
between an inner shell 46 and an outer shell 48. When
torque is applied to the inner shell 46 in a clockwise
direction, as indicated by an arrow 50, resistance of
the outer shell 48 due to a load will cause the
elastomer to shear, in-plane. Since the shear modulus
for elastomers is very small, the torque-carrying
capability of a spherical or cylindrical radial bearing
is very limited.
The second model is a bearing having a square
transverse cross-section and a center 52, as shown in
Figs. 4a and 4b. A layer of elastomer 54 is disposed
between an inner shell 56 and an outer shell 58. Fig.
4a represents the bearing in an unloaded state. When
torque is applied to the inner shell 56, about the
center 52 in a clockwise direction, as indicated by an
arrow 60, and the outer shell 58 resists, the inner
shell 56 is displaced slightly in the torquewise
direction - i.e., clockwise as shown in Fig. 4b. The
applied torque and consequent shi~t of the inner shell
56 causes the elastomer in a region 64, which is
torquewise "after" a corner 66, to be placed in
compression. The compressive reactive forces are
normal to the surface of the elastomer layer 54, as
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g
indicated by a vector 68. Since the reaction vector
68 "misses" the center 52, a moment is generated in
a direction counter to the applied torque.
In a~other region 70, which is torquewise "before"
a corner 72, the elastomer is strained in tension.
The tensile reactive forces of the elastomer 54 are
normal to the surface, as indicated by the vector 74.
Since the reaction vector 74 "misses" the center 52,
a moment is generated in a direction counter to the
applied torque. The reactive forces discussed
relative to regions 64 and 70 are typical for the
entire perimeter of the bearing and give the bearing
torsional stiffness.
The noncircular transverse contour of the bearing,
and consequent noncircular transverse cross-section
for the elastomer, causes the elastomer to bend
(compression and tension normal to the elastomer layer)
rather than to shear (in-plane) in response to applied
torque. Compression is readily reacted by an elastomer,
such as 85% natural rubber and 15% polybutadiene,
which has a compressive modulus on the order of hundreds
of thousands of pounds per square inch. Tension, on the
other hand, is reacted by the tensile strength of the
elastomer which is comparatively low, even though in
fatigue it is as much as six times the shear modulus.
Tension can be reduced to within acceptable limits by
bearing precompression, techniques for which are well
known in the manufacture of rod end bearings. Elastomer
bending rather than shearing, provides the bearing with
torsional stiffness so that torque may be transmitted.
The mechanics of this model with its one layer of
elastomer 54 are applicable to the bearing of ~ig. 2
~24~3~9
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with its several elastomer layers 16.
Returning to Fig. 2, torque is applied to the
inner shell 12 about the axis 20 in a clockwise
direction, as indicated by the arrow 76, and is resisted
by the outer shell I4~ The noncircular transverse
contour of the bearing causes the elastomer layers 16
to bend. Therefore, in a region 78 that is torque-
wise "after" a lobe, such as the lobe 34(38), compressive
reactive orces are exerted ~y the elastomer 16 as
indicated by the vectors 80-84 according to a distributed
hydrostatic pressure pattern under a dashed line 85.
Since pressure is normal to the surface, the vectors
80-8~ are focused at the origin 26 of the arc segment
30, thereby "missing" the axis 20 and creating a moment
counter to the applied torque. Similarly, in a region
86 that is torquewise "beore" a lobe, such as the lobe
39, tensile reactive forces are exerted by the elastomer 16
as indicated by the vectors 88-92 according to a dis-
tributed hydrostatic pressure pattern under a dashed
line 93. Again, since pressure is normal to the
surface, the vectors 88-92 are all focused away from
the point 26, thereby "missing" the axis 20 and creating
-~a moment counter to the applied torque. At a point 94
on the arc segment 30, which is midway between the lobe
34(38) and the lobe 35(39), there is a transition from
compression to tension where the reactive forces of
tension and compression are ZERO. The pattern of tension
and compression as described with reference to the arc
segment 30 is s;milar for the arc segments 31, 32 and 33.
Thus there is a transition from compression to tension at
each lobe and midway therebetween where thereactive forces
are ZERO. ~etween the points of ZERO reactive force,
the reactive forces increase in a textbook-calculable
manner that can be verified by finite element codes,
such as TEXGAP or NASTP~N, which adequately represent
the behavior of the elastomer. The pressure patterns
~2~34~
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shown are simply illustrative and it is desirable
to design a bearing for gradual ~radients within
the existing allowables for stiffness, thickness, etc.
Although the sum of the reac~ive forces around the
azimuth of the bearing is ZERO, the misfocusing
("missing" the axis 20) of the reactive forces causes
a nonZERO moment which can be calculated by integrating
the reactive forces and the distances by which ~hey
"miss" the axis 20 over the azimuth of the bearing.
It should be understood that the bearing is not
perfectly stiff and that some "winding up" (rotation
of the inner shell 12 relative to the outer shell 14
about the axis 20) will occur before equilîbrium is
reached. Because of "wind-up", the elastomer layers
16 are subject to shear, especially at the arc mid-
points (e.g., 94) and at the lobes. However, since
"wind-up" is limited, shear is limited and is well
within acceptable limits. As mentioned before, with
respec~ to the bearing of Fig. 4, the torsional stiff-
ness of the bearing of Fig. 2 derives from its noncir-
cular transverse contour which causes applied torque
to be reacted primarily in compression and tension
(normal forces) rather than in shear (in-plane force),
and tension is controlled by precompression. In fact,
it is desirable that the precompression is of larger
magnitude than the reactive tension so that there is
net compression.
As another example of torsional stiffness,
consider a bearing having inwardly-extending lobes, a
transverse cross-section of which is shown in Fig. 5.
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For descriptive simplicity, a single elastomer layer
100 is shown disposed between an inner shell 102 and an
outer shell 104, although several layers of elastomer
separated by nonresilient shims is more typical~ The
transverse contours of the exterior surface of the
inner shell 102 and interior surface of the outer shell
104 are generated by radii (R3) and (R4) from four
points 106-109 equally offset from, but symmetrically
distributed about the bearing axis llOr The radius
(R3) is less than the distance from the inner shell 102
to the axis 110, and the radius (R4) is greater than
the radius (R3) by the thickness o~ the elastomer 100.
This results in a transverse cross-section character-
ized by four inwardly extending lobes 112-115 between
which are four arc segments 116~119.
A model is used to visualize the reaction
stresses resulting from applied torque. In Fig. 6 is
shown a segment of a bearing having a stylized
inwardly-extending lobe 120. A layer of elastomer 122
is disposed between an inner shell 124 and an outer
shell 126. Fig. 6a represents the bearing in an
unloaded state. In response to torque applied in the
clockwise direction, as indicated by an arrow 128 in
Fig. 6b, the inner shell 124 shifts in the torquewise
direction, thereby causing the elastomer to bend so
that it is in compression in a region 129 which is
torquewise "before" the lobe 120 and in tension in a
region 130 which is torquewise "after" the lobe 120.
Applying the concepts of the model (or Fig.
6) to the bearing of Fig. 5, it is observed that torque
applied to the inner shell 102 in a clockwise direction,
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as indicated by an arrow 132, i5 reacted in compression
in a region 134 which i5 torquewise "before" the lobe
113 and in tension in a region 136 which is torquewise
"after" the lobe 112~ The reactive forces exerted by
the elastomer 100 are ZERO at the lobes and midway
therebetween and there is a limited amount of shear all
around. The distribution of forces, as described with
respect to the area 116 between the lobes 112 and 113,
is exemplary of the distribution about the entire
azimuth of the bearing. Much as in the example of the
outwardly-extending lobe embodiment discussed herein-
before, the reactive forces of compression and tension
exerted by the elastomer 100 are normal to the surface,
as indicated by the vectors 138-147, and therefore
"miss" the bearing centerpoint 1~0 so that a moment
is generated which is counter to the applied torque.
Likewise, precompression acting normal to the surface
reduces tension to within functional limits.
It should be understood that the number of lobes
is not limited to ~OUR, and that any design incorporating
the nearly-spherical, axially-lobed concept would be
useful for transmitting torque. However, at least
three lobes are required to preserve polar symmetry
for homokineticity. Furthermore, it should be under-
stood that the arc segment-generated lobes of ~igs. 2
and 5 are not intended as restricting, but rather as
illustrative of the teachings of this invention. A
bearing have a polygonal transverse cross-section,
such as illustrated in Figs. 4 and 6, would result in
"splines" rather than lobes, but as is evident from the
discussions relating thereto, would also benefit from
the teachings contained herein.
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TILTWISE STI~NESS
Thus far, the description of the invention has
focused on the transverse cross-section of the bearing.
~or maximum torque-carrying capability, the transverse
cross-section of the bearing at any position along the
longitudinal axis would be constant - resulting, for
instance, in a nearly cylindrical, splined or lobed
bearing. Howeverl this would be undesirable for a
constant velocity joint that must accommodate axial
angular misalignment (tilt) between a drive and a load.
Consider, for example, the coupling disclosed in U.S.
Patent No. 2,363,469 (Goldschmidt, 1943), entitled
FLEXIBLE COUPLING, ~LEXIBLE MOUNTING, AND THE LIKE
which, as shown in Fig. 4 t~erein, is essentially a
lobed cylindrical bearing. The purpose of that
coupling is for the torsional stiffness of the coupling
to increase progressively with rotation of one member
within another. However, such a configuration is
especially noncompliant in tilt. By contrast, it is
desirable that the constant velocity joint o~ this
invention be especially compliant in tilt.
Although the bearing of this invention is
applicable to rotating loads, tilt is discussed in a
"static" sense. As discussed hereinafter, tilt is
essentially accommodated in elastomer shear, which is
virtually unaffected by tension and compression.
It is known that a true spherical bearing will
provide maximum compliance in tilt. However, the
lobed transverse cross-section required for torsional
stiffness precludes that shape. Nevertheless, it is
desirable to "build-up" the bearing longitudinally
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~L24~3~9
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(axially) so that it is as nearly spherical as
possible. Generally, this is achieved by reducing the
transverse cross-section of the bearing toward its ends
according to a spherical function to give the bearing a
nearly spherical profile. There are several ways to
achieve this result. One way to achieve a nearly
spherical axial profile is to rotate each equatorial
arc-segment, such as the arc-segments 30-33 of Fig. 2,
about its associated arc-segment generating point, such
as the points 26-29 of Fig. 2. This provides an axial
contour that has essentially four centers on the
equatorial plane.
For a true sphere, the axial contour has only
one center. A bearing tilting about that center is
very compliant. By contrast, the axial contour of the
bearing of this invention has at least two distinct
centers, one for each arc-segment and none of which
coincide~with the bearing center, about which the bear-
ing tilts. (The bearing center can be defined as the
intersection of the axis 20 and the equatoriai plane.)
Therefore, the bearing of this invention is somewhat
stiffer than a true sphere.
Another way to achieve the nearly spherical
axial profile is to define cross-sections for each
norma] plane to the axis, reducing the cross-section
according to a spherical function in proportion to the
distance between the particular plane and the
equatorial plane - or, in other words, reducing the
cross-section towards the ends. This is readily
achieved by choosing arc-segment generating points for
each normal plane that correspond azimuthally to the
arc-segment generating points on the equatorial plane,
but that are successively
~ 2 4~ 3
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closer to the axis, and choosing correspondingly smaller
radii to generate the arc-segments. The offset of these
points from the axis may even be reduced to ZERO at a
truncated end, or edge, rather than at the "virtual"
end of the bearing. By generating each transverse
cross-section individually, rather than rotating each
equatorial arc-segment about its equatorial arc-
segment generating point, the centers of axial contour
are more vaguely defined and less coincident with the
bearing center, thus making the bearing somewhat stiffer
in tilt.
In any of the above examples for profiling the
bearing so that it is nearly spherical, the torsional
stiffness of the bearing is concentrated at the
equator - for it is there that the lobes are lar~er,
the amount of elastomer greater, and the moment arm
longer - and diminishes toward the ends. Thus the
choice of profiling technique may be based on con-
siderations such as a desired ratio of torquewise to
tiltwise stiffness, rather than strictly dictated by
maximizing or minimizing either, respectively. It
should be understood that the profiling techniques
discussed herein are applicable to either the inwardly-
lobed or outwardly-lobed bearing.
...
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CONSTANT VELOCITY JOINT
In ~ig. 7 is shown a constant velocity joint 150
employing the bearing o this invention, similar to
the bearing 10 of Fig. l. In other words, alternate
layers of elastomer 152 and shims 154 are interposed
between an inner race 156 and an outer race 158. The
inner race 156 has a flange 157 for attachment in a
suitable manner to a rotatable drive member 160 which
rotates about a drive axis 162 and the outer race 158
has a flange 159 for attachment in a suitable manner
to a rotatable load member 164 which rotates about a
load axis 166. The drive axis 162 is coincident with
a nominal joint axis which would correspond to the
bearing axis 20 of the bearing 10. The joint 150
accom~odates an angular misalignment between
the load axis 166 and the drive axis 162 by elastomer
shear. It should be understood that the drive and
load are simply illustrative, and may be interchanged.
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TAILaRING TILTWISE STIFFNESS
Consider the case of a nearly spherical, lobed
bearing, such as is illustrated in Fig. l. It is
readily apparent that the profile will vary somewhat
depending upon the azimuth from which the bearing is
viewed. In other words, the axial cross-section
through a pair of lobes will be slightly greater than
through the inter-lobal (arc segment) area. A larger
axial cross-section translates into a slightly greater
moment and slightly more elastomer resisting tilt.
Therefore, the tiltwise stiffness of the bearing at the
lobes is slightly greater than therebetween. Another
way to analyze the azimuthal variation in tiltwise
stiffness is to observe the behavior of the elastomer
at ninety degrees to the tilt - where it is essentially
twisted. For tilt through an arc segment between lobes,
the twist at ninety degrees is reacted in elastomer shear
at an arc segment. For tilt through a lobe, the twist
at ninety degrees is reacted at another lobe in both
shear and bending. As discussed with respect to torque,
the elastomer is stiffer in bending than in shear.
For certain applications, it is desirable to tailor the
tiltwise stiffness of the bearing so that it is uniform
for any azimuth.
According to one scheme for tailoring the tiltwise
stiffness of the bearing, the height of the bearin~, and
consequently its overall axial cross-section, is reduced
locally, at azimuths where the tiltwise stiffness other-
wise would be ~reater. This is illustrated in ~ig. 8
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which shows a bearing 170 having four outwardly-
extending lobes 172. The bearing 1~0 is essentially
the same as the bearing 10 of ~ig. 1, except that its
upper and lo~er edges 174 and 176 have been contoured
so that the height of the bearing varies according to
azimuth. The uncontoured ends 22 and 24 of the bearing
10 of Fig. 1 are indicated by dashed lines. At the
lobes 172 the height of the bearing is reduced, and it
i5 maximum therebetween. Since the upper and lower
edges 174 and 176 contribute little to the torsional
stiffness of the bearing 170, the ad~erse effect of
contouring on the torque-carrying ability of the bearing
170 is not profound and, if needs be, can readily be
accommodated by overall bearing sizing, as discussed
hereinafter. The precise contour required for a
constant tiltwis~ stiffness at all azimuths is textbook
calculable and verifiable according to finite element
codes as discussed hereinafter. It should be under-
stoo~ that uniform tiltwise stiffness can be achieved
by contouring only one of the ends (edges), but that
contouring both preserves polar symmetry.
Another technique for tailoring tiltwise stiffness
of the bearing of this invention is to vary the duro-
meter of the elastomer locally, according to azi~uth, so
that lower durometer (softer) elastomer is used in areas
that otherwise (with uniform durometer elastomer) would
be stiffer. Consider, in Fig. 9, a partial transverse
cross-section of a bearing 180 which is essentially
similar to the bearing of Fig. 2. The elastomer 182
at a lobe 184 is softer, and hence more compliant,
than the interlobal elastomer 186. Bearing construction
techniques are known wherein approximately eighty
:~Zg~f~3~9
-20-
percent of the elastomer is inserted into the bearing
as a solid sheet (calendar), and the remainder is
injected as a liquid, thereafter to cure. These
techniques are well-adapted for implementing this
technique for tailoring tiltwise stiffness. A reduction
of durometer at the lobes will impact torsional stiff-
ness as well as tilt~ise stiffness. However, Fig. 2
illustrates that the reactiYe forces of compression and
tension, which account for the torsional stiffness of
the bearing, are minimum at the lobes. Therefore, the
impact upon torsional stiffness of using lesser duro-
meter elastomer at the lobes is minimized and, as in
the previous example, can be accounted for by initial
bearing sizing considerations.
A variation to the technique of locally varying
the durometer of the elastomer is to provide a region
of higher durometer (stiffer) elastomer at the ends -
- in other words, a band around the circumference - and
varying the extent, or height, of the band locally to
offset bearing stiffness variations. The higher dur-
ometer edges would also reduce elastomer bulging.
Yet another technique for tailoring tilt is to vary
the thickness of individual elastomer layers locally, at
certain azimuths - making the elastomer thinner at
azimuths where the bearing otherwise would be stiffer,
such as at the lobes. Consider ~ig. 10, a partial
transverse cross-section of a bearing 190 which is
essentially similar to the bearing of Fig. 2. The
elastomer 192 at a lobe 194 is thinner, and hence more
compliant, than the interlobal elastomer 196. This is
indicated by a dashed line 197 that indicates the
contour for uniform elastomer thickness. The thickness
of a particular elastomer layer is determined by the
~2~L~3'~
space between the shims (or, in the case of the outer-
most elastomer layers, by the space between a shim and
the bearing race). Therefore, to reduce the local
thickness of an elastomer layer, the local thickness
S of the adjacent shim(s) is increased. This is readily
implemented when composite technology is applied to the
manufacture of the shims, as discussed hereinafter.
Increasing the shim thickness at a lobe will also have
the effect of strengthening the shim locally, which is
expedient in light of the pressure gradient at the lobes.
Depending upon the application, one or more elastomer
layers need to be reduced in thickness locally to make
the tiltwise stiffness uniform at all azimuths. It
should be understood that varying the thickness of a
shim will alter its transverse contour and, hence, the
focusing of the reactive forces of tension and com-
pression as discussed with reference to Fig. 2, and will
affect torsional stiffness according to that mechanism
as well as from reduced layer thickness. However J the
lobes per se contribute little to the torsional stiff-
ness of the bearing since the reactive forces of
compression and tension are minimum thereat. Never-
theless, these effects may be accounted for in initial
sizing considerations.
-
34~
-22-
GIMBAL-LIKE ROTOR SYSTEM
Thus far, the description of the in~ention has
focused on the torquewise and tilt~ise stiffnesses of
the nearly-spherical, lobed bearing of this invention.
Those characteristics, in addition to the homokineticity
of the bearing, make it useful for certain
applications, especially in light of the teachings
relative to tailoring tilt, whereby the tiltwise stiff-
ness can be made uniform for all azimuths so as not to
introduce vibrations in a rotational load coupled to
the bearing.
Consider a helicopter gimbal rotor systern wherein
a portion of rotor 1apping is accommodated
by tilting a rotor hub relative to a rotor shaft, rather
than through individual, articulated flap hinges for
each blade. As discussed previously, a Hooke
; joint can accommodate both high torque and tilt,
but introduces cyclic pulsations in the load which, in
; the context of a helicopter, would be extremely undesir-
able not only from a viewpoint of passenger-comfort but,
more fundamentally, from a control viewpoint. Therefore,
it is known to provide a rotor system with a gimbal
bearing, such as a ball joint, to accommodate
flapping, and separate means, such as a torque-rigid
boot to supply driving torque to the rotor. Examples
of these systems are discussed in U.S. Patent No.
4,323,332 (Eradenburgh, 1982), entitled HINGELESS
HELICOPTER ROTOR WITH ELASTIC GIMBAL HUB. By contrast,
the nearly-spherical, axially-lobed bearing of this
invention offers the possibility for accommodating
torque and tilt (flap) in a single cornpact component,
thereby reducing size, parts count, and complexity,
while providing the benefits of elastomeric bearings.
~IL2~3~
.
-23-
The heli.copter rotor system of Fig. ll comprises
four blades 200 attached via a hub 202
to a rotorshaft 204. I.t should be understood that the
number of blades is not limited to FOUR. A blade 200
i5 attached at its root (inboard) end to a torque tube
206 which is essentially a hollow, torsionally stiff
sleeve that is flattened at its blade-attaching
(outboard) end to mate with the blade 200. The other
(inboard) end of the torque tube 206 is adapted to
connect, via a bearing 208, to the hub 202 at a flange
210. The bearing 208 is any suitable bearing, such as
a radial elastomeric bearing or a conventional (metallic)
spherical bearing (as shown) that allows for rotation
of the torque tube 206 about a blade pitch (longitudinal)
axis. As will become evident, it is not necessary for
the torque tube 206 or the bearing 208 to accommodate
blade centrifugal loads.
A control rod 212 is responsive to pilot and/or
automatic flight system commands via actuators and a
swash plate (neither are shown). The rod 212 is
connected via a pitch link (horn) 213 to the inboard end
of the torque tube 206 so that linear rod motion is
translated into rotary blade pitch changing motion
which is imparted, via the torque tube 206, to the
blade 200.
A longitudinal spar 214 is attached a~ its inboard
end to the hub 202 at the flange 210. At its other
(outboard) end the spar 214 is attached in a suitable
manner to the blade 200, at or near the point where
the blade 200 is joined to the torque tube 206. The
materials and configuration for the spar 214 are
selected to be torsionally compliant so as to accommo-
date blade pitch changes, and to be relatively stiff
~Z~L~3'~
-24-
when bending in response to blade flapping and even
stiffer in response to lead/lag motions. The spar 214 may
comprise an I-beam formed of composite materials which
complies with t~ese design paramaters. Blade centrif-
ugal forces are reacted along the length of the spar214 rather than in the torque tube 206.
As mentioned hereinbefore, it is a fundamental
principle of gimbal rotor systems that the
hub accomm~dates at least a portian of the overall
rotor flapping. Therefore, the hub 202 is pivotally
attached for flapping to the rotor shaft 204, in the
following manner, making the rotor system of this
invention a "gimbal-like" rotor.
The hub 202 is essentially a bearîng (joint) that
is similar to the bearing lO of ~ig. 1. In other words,
the hub 202 comprises an inner shell 216 (compare 12),
an outer shell 218 (compare 14), and alternate layers
of elastomer 220 (compare 16) and non-resilient shims
222 (compare 18) interposed at increasing radii there-
between. The number of layers is not limited to thenumber shown.
The torque handling ability of the hub 202 derives
from longitudinal lobes 223 that affect the transverse
cross-section of the elastomer layers, which has been
discussed in detail hereinbefore. The main difference
between the hub 202 and the bearing lO (of Fig. 1) is
in the exterior (facing away from the elastomer) faces
of the shells (races). It should be understood that
the outer shell 218 distributes the driving torque to
all blades 200 essentially equally, regardless of
whether the lobes are located at the blades or inbetween.
It is not even necessary that the number of blades equal
the number of lobes, or vice-versa.
3~9
-25-
The exterior surface of the inner shell 216 is
provided with a flange, such as a flat annular flange
224, that is suited for attachment, such as by bolting,
to a mating surface on the rotorsha~t 204 to receive
dri~ing torque therefrom. The inner shell 216 is
coaxial with the rotor shaft 204.
The exterlor surface of the outer shell 218 is
provided with the flanges 210 for attachment of the
spar 214 and the torque tube 206. Since blade centrifu-
gal forces for all four blades 206 are transmitted alongthe respective spars 214, the blade centrifugal forces
are reacted entirely by the outer shell 218. Therefore,
the outer shell ~ust be sized accordingly, especially
in thickness. In the case of a composite (nonmetallic)
outer race 218, fiber orientation can be used
advantageously.
Thus, in the rotor system,torque and flapping are
accommodated by a single bearing (joint). Lead/lag
motions are accommodated tdamped) by bearing windup, as
discussed hereinbefore. It should be understood that
flapping is shared between the hub 202 and the spar 214 -
for instance, 70% and 30% respectively. The rotor
system shown and described is simply illustrative of an
application for the joint of this invention and many
other rotor configurations would benefit from the use
of the joint. `'~lap" in the context of a rotor system
is the equivalent of `'tilt" as discussed hereinbefore.
Insofar as particular lobe geometries are concerned,
either inwardly or outwardly extending lobes are well
suited to the use of the bearing of this invention in
a helicopter gimbal-like rotor system. Design
particulars will depend largely upon individual applica-
tions. ~or instance, the ratio of torquewise stiffness
to tiltwise stiffness can be established, as well as
edgewise natural frequencies.
3~
-26-
ACCOMMODA~ING AXIAL LOAD
The previous discussions regarding torsional
stiffness, tiltwise stiffness, homokineticity, and
centrifugal loads are all very relevant to the
incorporation of the bearing of this invention in a
helicopter gimbal-like rotor system. However, unlike
many other systems involving the coupling of a drive
to a load, in a rotor system there is an additional
requirement that the bearing bê able to
accommodate an axial load such as the lift generated
by the rotor.
Generally, the load-carrying ability of an
elastomeric bearing is related to the cross-section
and orientation of the elastomer layers relative to the
load. For instance, a rod end bearing, which is
essentially a spherical bearing trunca~ed at two opposite
ends, is subjected to radial loads that are reacted in
elastomer compression on one side of the bearing and in
elastomer tension on the opposite side. As discussed
hereinbefore, elastomer tension is reduced by pre-
compression. By contrast, in the case of the bearing
of this invention, the end where an axial load could
most effectively be reacted ~i.e., in elastomer
compression) is truncated. One approach to reacting
an axial load would be to not truncate the bearing on
the end in compression - leaving only the opposite end
(in tension) truncated to accommodate attachment to the
inner race (shell). In the rotor system of Fig. 11,
this would mean not truncating the rotorshaft-end of
the bearing, but that is clearly not possible.
A first order solution to the problem of accommodat-
ing axial load is to truncate as little as possible on
the end of the bearing that would otherwise react an
~gLi3~9
-27-
axial load in elastomer compression. ~owever, there
is an inherent limit to this approach L~posed by the
size of the drive and the range of tilt.
In the case where both ends of the bearing are
truncated9 there is no elastomer where it would be
most useful. An ancillary problem to the diminished
ability of such a bearing to accommodate an axial load
is that the load will cause an axial distortion of the
bearing - in other words, successive layers will be
increasingly displaced (offset~ axially in response to
the axial load - and a consequent stiffening o the
bearing in tilt. It should be understood that axial
loads can be in one of two opposite directions, either
tending to push together or to pull apart the drive and
load members. The latter, which exert a separating
force, are discussed, but the teachings are equally
applicable, in an opposite sense, to the ormer.
In Fig. 12 is shown a partial axial cross-section
of a bearing which accommodates a separating axial load
without stiffening in tilt. The bearing is comparable
to the hub bearing in the gimbal-like rotor system of
Fig. 11 except that Fig. 11 does not disclose the
following feature, and six elastomer layers are shown,
rather than only two. The separating axial load is
the equivalent o rotor lift and is indicated by a
force applied to the outer race 218, in the upward
direction as indicated by an arrow 224, that is resisted
by the inner race 216.
Without the feature, the centers of axial contour
for each elastomer layer would be coplanar - on the
equatorial plane - for maximum tiltwise compliance.
~2~34g
With the feature, the bearing is manufactured
with each successi~e layer 220 of elastomer, and hence
each successive shim 222, offset increasingly away
from the load at increasing radii. In other words,
the most inward elastomer layer has its centers of
axial contour disposed on the equatorial plane 226.
The nex~ outward elastomer layer is of increased
radius, as discussed hereinbefore, and has its centers
of axial contour disposed on a plane 228 which is off-
set from the reference plane in a direction away fromthe applied, separating axial load. Each succeeding
elastomer layer is disposed so that its centers of
axial contour are on a plane which is offset from the
reference plane in a direction away from the applied,
separating axial load. One result of this configuration
is that the elastomer is thicker at the end of the
bearing which is away from the load and reacts the load
in compression.
When separating axial load (LI~T) is applied to
the bearing, the outer race 218, and each successive
elastomer layer yield in the direction of the load,
thereby bringing together the centers of axial contour.
Ideally, the offset is perfectly matched to the load
so that the centers of axial contour all coincide on
the equatorial plane 226 under load, and tiltwise
stiffness is thereby minimized. However, with varying
loads, such as are inherent in a helicopter rotor
certain design compromises may be necessary. But these
are all accommodated in the initial sizing of the
bearing.
~L2~3~
-29-
Since the centers of axial contour coincide less
without an axial load, the bearing is stiffer without
a load and softer with a load. This is ideal for a
helicopter. For instance, when the helicopter is
parked or taxiing, the rotor is stiff in tilt so that
wind gusts do not cause mast bumping. For in-flight
maneuvering, the rotor is more compliant in flap.
The essential characteristic of this feature is
that the elastomer layers are progressively offset
axially in a direction away from an anticipated axial
load so that the load causes the layers to be less
offset. The offset causes more elastomer to be placed
in compression to accommodate the load. It should be
understood that this feature is independent of the
lobes - in other words, the feature would be useful in
the context of a spherical bearing that does not have
axial lobes and which, consequently could not handle
high torque'loads.
It should be understood that the basic invention
relates to a nearly spherical lobed bearing that
accommodates torque and tilt and that acts as a constant
velocity joint. The function of the bearing is improved
for certain applications by making the tiltwise stiff-
ners uniform at all azimuths and enhancing the axial
load carrying capability of the bearing. For instance,
the improvements are useful, but not absolutely
essential, in the context of applying the bearing, or
joint, to a gimbal-like rotor system. There are many
applications for the basic bearing, sans the
improvements.
:~24~i349
-30-
MANUFACTURING TECHNIQUES
As mentioned hereinbefore, several alternating
layers of elastomer and non-resilient shims are
disposed between the races. Generally, these materials
and the methods by which they are assembled together
with the races are well known. For instance, rubber
compounds are well suited for the elastomer and they
may be injected at high pressures into the bearing
during manufacture to effect precompression. It is also
known to vary durometer from layer-to-layer to maximize
fatigue life. It is evident that for certain bearing
geometries, it will be necessary to split the shims
during ~anufacture so that they may be inserted into
the bearing. Splitting the shims and staggering ~he
gaps are well known - for instance, in the art of rod
end bearings. Also, the shims must be thick enough to
maintain their dimensions during high compression
molding.
In the general case, the shims will be of uniform
thickness and their shape will correspond to the con~our
of the races. However, in applications where it is
desirable to reduce the elastomer thickness in an area,
it is desirable to vary the shim thickness. In these
cases, a composite layup, such as graphite/epoxy, is
well suited for the shim, especially in conjunction
with computerized design and manufacture facilities.
It should be understood that the shims are exposed
to the reactive forces of tension and compression (i.e.,
bending - as discussed hereinbefore). Bending moments
create high hoop stresses and are of concern in shim
design. For instance, in U. S. Patent No. 4,142,833
~Z4~i3~9
-31-
(Rybicki, 1979), entitled ELASTOME~IC BEARING FOR
HELICOPTER ROTOR, the laminate geometry is designed
to reduce laminate bending. By contrast, the
geometry of the bearing of this invention is
specifically intended to cause laminate bending.
This simply means that the shims must be designed
accordingly.
"In the initial sizing of bearings for design
trade-off studies, the analytical techniques involve
simple methods based upon conventional strength of
material approaches. Average pressures and strains
are calculated using handbook formulas and average
elastomer criteria for shape factor and modulus.
Empirical formulas, based on gross assumptions of
bearing construction, are available to establish
initial overall size Bearing stiffness can be
calculated, using handbook techniques, to determine
compatibility with the specific application. After
the bearing's external envelope is defined in this
manner, specific details of the laminate package can
then be defined. Shim thickness and elastomer laminate
thickness and modulus can be selected on the basis of
balanced elastomer strains and/or stiffness, and by
shim bending stresses. Simplified geometry and
idealized loading assumptions are required at this
stage of the analysis for purposes of design iteration.
Bearing loads and/or motions must be applied individually
and added vectorially or stresses must be superposed to
establish a basic understanding of the combined (shim)
or elastomer stresses.
"This methodology does not account for the non-
linear stress-strain behavior of the elastomer, nor for
the non-linearities involved in the analysis of any
~Z~63~9
-32-
large strain problem. In addition, many bearings
under load have non-axisymmetric geometries and
non-axisymmetric loadings. Finite element techniques
are required to obtain a better understanding of this
three-dimensional highly non-linear analytic problem.
Computer codes have been developed, based on programs
like TEXGAP (and NASTRAN) which are capable of
handling some of the problems involved in this
analysis. They contain elements which are formulated
to reflect the incompressible behavior of elastomers
(Poisson's ratios near .5). The entire bearing can
also be modeled. A more accurate definition of the
stress/strain within the bearing can be obtained under
various combinations of loading. Local and edge effects
can be more accurately evaluated. The bearing design
can be refined to obtain a better balance of elastomer
strains across the bearing and to minimize shim
stresses." (American Helicopter Society Journal,
January 1981, p. 37; The Sikorsky Elastomeric Rotor,
R. Rybicki)
Although the invention has been shown and des-
cribed with regard to particular embodiments, it should
be understood that various changes and additions could
be made therein and thereto without departing from the
spirit and scope of the invention.
